Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2011.164
URN: urn:nbn:de:0030-drops-33451
URL: https://drops.dagstuhl.de/opus/volltexte/2011/3345/
Fomin, Fedor V. ; Philip, Geevarghese ; Villanger, Yngve
Minimum Fill-in of Sparse Graphs: Kernelization and Approximation
| pdf-format: |
|
Abstract
The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop kernelization algorithms for the problem on several classes of sparse graphs. We obtain linear kernels on planar graphs, and kernels of size O(k^{3/2}) in graphs excluding some fixed graph as a minor and in graphs of bounded degeneracy. As a byproduct of our results, we obtain approximation algorithms with approximationratios O(log{k}) on planar graphs and O(sqrt{k} log{k}) on H-minor-free graphs. These results significantly improve the previously known kernelization and approximation results for Minimum Fill-in on sparse graphs.
BibTeX - Entry
@InProceedings{fomin_et_al:LIPIcs:2011:3345,
author = {Fedor V. Fomin and Geevarghese Philip and Yngve Villanger},
title = {{Minimum Fill-in of Sparse Graphs: Kernelization and Approximation}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
pages = {164--175},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-34-7},
ISSN = {1868-8969},
year = {2011},
volume = {13},
editor = {Supratik Chakraborty and Amit Kumar},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2011/3345},
URN = {urn:nbn:de:0030-drops-33451},
doi = {10.4230/LIPIcs.FSTTCS.2011.164},
annote = {Keywords: Minimum Fill-In, Approximation, Kernelization, Sparse graphs }
}
| Keywords: | Minimum Fill-In, Approximation, Kernelization, Sparse graphs | |
| Seminar: | IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011) | |
| Issue date: | 2011 | |
| Date of publication: | 01.12.2011 |
